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双道窄入口完全非对称排他过程中自发对称破缺现象的研究

Spontaneous symmetric breaking in two-lane totally asymmetric simple exclusion process with narrow entrances

  • 摘要: 研究了双道窄入口完全非对称排他过程.运用了集簇平均场理论来研究了自发对称破缺现象,该方法考虑了2N个格点之间的相关性.研究结果显示非对称低密度/低密度相是不存在的;随着每道格点数N的增加,理论分析结果越来越接近蒙特卡罗模拟结果。此外,系统中各相的边界均呈现指数变化,据此变化得到了各相边界理论分析的精确值,这些精确值与大尺寸系统下的模拟结果非常吻合.在该模型中,入口和出口处粒子之间相互作用的强度用p来表示,当p比较大的时候,该系统才会产生自发对称破缺现象.在集簇平均场理论分析中,非对称的高密度/低密度相对应的最大入口概率值随着p的增加而呈现指数衰减的特征,据此可以得到非对称的高密度/低密度相消失时对应的临界p值.此外,随着N的增加,得到的不同的临界p值也呈现指数增加的特征,据此可以得到临界p值的精确分析值,该分析值与模拟值也非常吻合.

     

    Abstract: Two-lane totally asymmetric simple exclusion process (TASEP) with narrow entrances was studied. The N-cluster mean field analysis was carried out for spontaneous symmetric breaking, in which correlation of 2N sites was considered. The analysis indicates that asymmetric LD/LD(low density/low density) phase does not exist. With increase of N, the analytical results are getting closer to the Monte Carlo simulation ones. In addition, it was found that the boundaries between the phases all exhibit exponential change, which enables us to predict the boundaries in the exact solution, and it was shown that the predicted results are in good agreement with the large size simulation ones. The spontaneous symmetric breaking exists when interaction between particles represented by parameter p is strong enough. It was found that the maximum values of entrance rate of asymmetric HD/LD(high density/low density) phase obey exponential decay with increase of p, and the critical value beyond which the asymmetric HD/LD phase disappears can be obtained in every cluster mean field analysis. What’s more, the critical values exhibit exponential increase with increase of N, and the exact solution of the critical value was also predicted. It was shown that the predicted critical value is also in good agreement with that obtained from simulations.

     

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